Zipping-Depinning: Dissolution of Droplets on MicropatternedConcentric RingsJose M. Encarnacion Escobar,*,† Erik Dietrich,‡ Steve Arscott,§ Harold J. W. Zandvliet,‡
Xuehua Zhang,*,∥ and Detlef Lohse*,†,⊥
†Department of Physics of Fluids and ‡Department of Physics of Interfaces and Nanomaterials, University of Twente, P.O. Box 217,7500AE Enschede, The Netherlands§Institut d’Electronique, de Microelectronique et de Nanotechnologie, CNRS, The University of Lille, Villeneuve d’Ascq 59652,France∥Department of Chemical & Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2R3, Canada⊥Max Planck Institute for Dynamics and Self-Organization, 37077 Goettingen, Germany
ABSTRACT: The control of the surface wettability is of greatinterest for technological applications as well as for thefundamental understanding of surface phenomena. In thisarticle, we describe the dissolution behavior of droplets wettinga micropatterned surface consisting of smooth concentriccircular grooves. In the experiments, a droplet of alcohol (1-pentanol) is placed onto water-immersed micropatterns. Whenthe drops dissolve, the dynamics of the receding contact lineoccurs in two different modes. In addition to the stick-jump mode with jumps from one ring to the next inner one, our studyreveals a second dissolution mode, which we refer to as zipping-depinning. The velocity of the zipping-depinning fronts isgoverned by the dissolution rate. At the early stage of the droplet dissolution, our experimental results are in good agreementwith the theoretical predictions by Debuisson et al. [Appl. Phys. Lett. 2011, 99, 184101]. With an extended model, we canaccurately describe the dissolution dynamics in both stick-jump and zipping-depinning modes.
■ INTRODUCTION
Wetting on structured surfaces is of great importance in manynatural, technological, and industrial processes. This holds forthe control of droplets for self-cleaning,2,3 antifogging,4 anti-icing,5 water harvesting,6 phase change heat transfer,7−9
evaporative self-assembly of nanomaterials,10−13 manipulationof micro- and nanosized objects,14 construction of circuits,15−18
or droplet-based analysis and diagnostics,19 among manyothers. Correspondingly, significant advances have beenachieved in the fundamental understanding of drop dynamicson a variety of microstructures.20−28 Several modes of dropevaporation have been observed, including constant contactangle, constant contact radius, stick-slide mode, and stick-jumpmode.29−32 Pinning at the contact line of the drop, thesurrounding fluid phase, and properties of the substrate are allessential to control the evaporation and dissolution modes andtransitions between them.33−38 Chemical or geometrical surfacefeatures even down to sub-nanometer scale may give rise topinning effects, imparting the lifetime of the evaporating ordissolving sessile drops.39,40
The mechanical stability and lifetime of drops may bepotentially tuned by well-defined surface structures. Among avariety of surface microstructures, engraved concentricmicrorings may pin the entire three-phase boundary of adrop, representing an interesting case of an extremely strongpinning effect. It was reported that microring structures are the
most effective in stabilizing droplets against mechanical andchemical perturbations, compared with other microtopo-graphical features of trenches or plateaus.19 Such stability ofdrops is highly desirable, e.g., for the hanging drop techniquefor long-term cell cultures19 and other techniques for analyticaland clinical diagnostic screening.41
To understand the dynamics of drops on the substratepatterned with concentric microrings, Kalinin et al.42 measuredcritical apparent advancing and receding angles and correlatedthem with the morphological characteristics of the rings. Theyfound that the apparent critical angles were independent of thering height and width, but were determined primarily by theslope of the ring sidewalls.42 Debuisson et al. quantitativelyshowed that concentric microrings facilitate the stick-jumpmodel of evaporating drops. They also found that for a givendroplet radius, the smaller the spacing of the rings, the shorterthe evaporation time. It was shown that the contact line depinswhen the liquid micromeniscus simultaneously touches bothsides of the groove (Figure 2). Assuming volume conservationduring jumping of the contact line to the next ring, a model wasdeveloped to explain the contact angle hysteresis.1 Debuisson etal. also showed that the contact angle hysteresis and the
Received: January 24, 2018Revised: March 19, 2018Published: April 13, 2018
This is an open access article published under a Creative Commons Non-Commercial NoDerivative Works (CC-BY-NC-ND) Attribution License, which permits copying andredistribution of the article, and creation of adaptations, all for non-commercial purposes.
evaporation behavior of the drop can be further modified byintroducing a gap as an artificial defect on the ring.44
In this work, we focus on the depinning behavior of dropletsfrom the microrings during the dissolution in a partiallymiscible liquid surrounding phase. We extracted the contactangles as a function of time from the experimental data andcompared them with the predictions by Debuisson et al.1 Wefound that this model works well for the case when thetransitions from ring to ring occur on a time scale much shorterthan the corresponding shrinkage of the droplet. However,when the time scales become comparable, our results revealanother mode of zipping-depinning (ZD). As far as we know,this new mode has not been reported in the literature yet. Wetheoretically analyze this zipping-depinning mode and canquantitatively describe the overall dissolution.
■ EXPERIMENTAL SECTIONThin glass substrates with thickness of 170 μm were used as thesubstrate, which are optimal for confocal microscopic imaging. Thefabrication of the micropatterned surfaces was done using a standardphotolithography process on the thin glass slides. The concentric ringsare at a distance of 50 μm from each other. The detailed protocol wasreported in a previous work.43
The experiments were conducted in a transparent container withdimensions 5 × 5 × 5 cm3, as sketched in Figure 1a,b, next to an imageof one of the substrates used (Figure 1c). Before each experiment, thetank was cleaned thoroughly using isopropylalcohol (Sigma-Aldrich)and water. The container was first filled with purified water (MerckMilipore, 18.2 MΩ cm), and then the substrate was immersed in thewater. A droplet of 1-pentanol was carefully placed on the center of theconcentric rings on the surface by using a glass syringe with a longaluminum needle with a diameter of 210 μm. The dispensing rate ofthe drop was controlled by a syringe pump.In all experiments, the images of the drop were recorded from a side
and bottom view. The side view of the drop was taken underillumination of a collimated light with a CCD camera through a longworking distance microscope lens, from which the contact angles andheight of the drops were extracted. The bottom view was taken with aconfocal microscope (Nikon A1+) in a transmission mode. In themeasurements, we monitor the shape of the droplet on the solidsurface and the contact line of the droplet during the dissolutionprocess.
■ EXPERIMENTAL RESULTSPinning and Depinning Condition. The definitions of all of the
parameters and notations in this work are shown in Figure 2. θ is thereal contact angle, measured with respect to the tangent of thesubstrate and θ is the apparent contact angle measured with respect tothe flat substrate. θr stands for the receding contact angle and θ* forthe contact angle at the depinning condition, which is also theapparent contact angle at the depinning condition. The drop is of 1-pentanol, and the surrounding phase is water.
In the early stages, the drop dissolves in a stick-jump mode (seeFigure 3). The jumps are triggered by the geometrical depinningcondition as shown in Figure 2. When the contact line encounters adefect, a transition to the constant contact radius mode is observed.The drop will shrink by decreasing simultaneously the height andcontact angle, while its footprint area remains constant (Figure 2a). Asthe drop dissolves, the actual contact angle θ is larger than thereceding angle, θr, as shown in Figure 2a (θ > θr). We note that therelative contact angle is measured with respect to the flat part of thesubstrate, i.e., the groove-free surface. As the contact angle reaches acritical value, i.e., the depinning contact angle θ*, the surface of thedrop touches the other side of the groove (Figure 2b), creating a newcontact line with a new effective contact angle θ*. The new contactangle θ* is much smaller than the receding contact angle at that point(θ* ≪ θr), causing the detachment of the contact line from the ring.The full contact line depins from the ring “at once” (jump phase of thestick-jump mode), i.e., we cannot temporally resolve any spatialvariation of the jump in azimuthal direction. In this case, the contactline moves uniformly in the radial direction until it encounters a newgroove and becomes pinned again (see Figure 2a). The main featuresof each phase in the stick-jump mode are consistent with thedepinning process of evaporative drops on the ring micropatterns.1,43
Figure 1. (a) Schematic diagram of a dissolving drop on microrings in the experiments. (b) Setup to observe the dissolution process. The dissolvingalcohol droplet immersed in water was imaged from side and bottom to extract data about both the contact diameter and contact angle. (c) Bottomview of microring patterns with a spacing of 50 μm.
Figure 2. Illustration of the movement of the contact line across asmooth defect. The drop shrinks toward the center on the left. Darkblue represents the bulk of the alcohol droplet, whereas light bluerepresents the bulk of the water in which the drop is immersed (a)receding contact line (at a time t1) and pinned contact line (at a timet2). (b) Condition for depinning (at a time t3), where θ is the realcontact angle, measured with respect to the tangent of the substrate, θis the apparent contact angle measured with respect to the flatsubstrate, the subindex “r” stands for receding, and the super index “*”indicates the depinning condition. θ* is the contact angle at the newcontact line.
Zipping-Depinning Mode and Self-Centering. At the late stageof drop dissolution, we observed the new zipping-depinning (ZD)mode. An example is shown in Figure 4. This mode is the result of themovement of the contact line constrained by the concentric rings.During this movement, part of the contact line remains pinned to thering, while a section of the contact line has already moved and pinnedto the following ring. This creates two fronts of the contact linebetween both rings (see Figure 4a). These fronts recede in theazimuthal direction, following the rings, until the entire contact linedetaches from the outer ring. We refer to these fronts as zipping-depinning fronts (ZDFs). At t = 0 s, the contact line is fully in contactwith an outer ring. At t = 0.2 s, the snapshots clearly show that only a
part of the contact line depins and pins at the following ring, whereasthe rest of the contact line remains pinned at the outer ring. Thesefronts recede along the rings, and a larger portion of the contact linezipped off at t = 0.4 and 0.6 s. Eventually, the two fronts meet eachother and the entire contact line detaches from the outer ring. Werefer to this mode as the zipping-depinning (ZD) mode and thesefronts as zipping-depinning fronts (ZDFs) (see Figure 4).
In practice, the drop is not always perfectly centered (imperfectcentering of the needle and wetting of the substrate). The off-centereddrop unzips more than one ring at the same time. This scenario issketched in Figure 5a next to an experimental example (b), where thereceding fronts of the unzipping contact line recede between two
Figure 3. Stick-jump mode. (a) Sketch of the stick-jump model. (b) Experimental side and bottom view images of the drop in the stick-jump mode(synchronized). Scale bar in side view images: 150 μm. The distance between rings is 50 μm. Scale bar in bottom view images: 500 μm.
Figure 4. Zipping-depinning model. (a) Scheme of zipping-depinning mode. (b) Snapshots of consecutive experimental pictures of the drop at fourdifferent times, revealing the zipping-depinning behavior with the azimuthal angle ϕ(t) between the ZDFs growing. (c) Illustration of the geometricmodel as two portions of spherical caps having the same the apex but different radii. As the ZDFs advance, the angle ϕ(t) increases with a rate ω(t) =dϕ/dt.
Figure 5. (a) Illustration of the self-centering process. The mass loss from the drop leads to zipping-depinning and hence to self-centering of thedrop. The red arrows show the typical azimuthal movement of the zipping-depinning fronts during the self-centering process. (b) Experimentalexample of the self-centering process shown in four bottom view frames taken at intervals of 34.8 s.
adjacent rings. In this process, the mass loss during the dissolution ofthe drop leads to a slow (as compared with the stick-jump mode)sequence of zipping-depinning-like movements along the biggerdiameter rings until the droplet self-centers; see Figure 5b. We referto this process as a self-centering process. The size of the droplets islarge compared with the spacing between the rings and the size of thegrooves. So, in this case, the relative change in volume associated withthe movement of the zipping-depinning fronts is relatively small.Moreover, the contact angle is larger than that observed beforedepinning, implying smaller dissolution rates.45 The movement of thecontact line is much slower than thatas we shall see belowobserved in the case of the zipping-depinning during the later stages ofthe dissolution process; see Figure 5b.
■ THEORETICAL ANALYSIS OF ZIPPING-DEPINNINGMODE
The contact angle θ during the entire dissolution process isplotted as a function of time in Figure 6. The apparentdepinning contact angle θ* before each depinning was constantat the value of ≈12°. Using this apparent depinning contactangle of θ* ≈ 12°, we calculate the angles θ2. Here, θ2 is theangle of the drop immediately after the jump.We assume that the jumps are instantaneous and that the
drop volume during the jump is conserved. The drop volumeimmediately before the depinning is then given by
θπθ
θ θθ
* =*
* + *+ *V r
r( , )
3sin
2 cos(1 cos )1 1
13
2(1)
where r1 is the radius of the patterned ring and θ* is thedepinning contact angle. Using the same expression, we cancalculate the contact angle θ 2 corresponding to a droplet withthe same volume but with a radius r2. Here, the indices 1 and 2correspond to the rings before and after the jump, respectively.From volume conservation V1(θ*, r1) = V2(θ2, r2), we obtain
πθ
θ θθ
πθ
θθθ*
* + *+ *
=
+ +
r r3
sin2 cos
(1 cos ) 3sin
2 cos(1 cos )
13
223
22
2
22
(2)
The predicted contact angles are plotted together withexperimental data in Figure 6, showing good agreement forθ2 at the early stages up to the drop radius of R ≈ 500 μm.However, in the later stage of the dissolution process, θ2 turns
out to be significantly smaller than the predictions. Thetransition from ring to ring in the experiments takes more timethan the theoretical prediction. This significant discrepancysuggests that the stick-jump mode is not accurate enough toaccount for the entire dissolution process. Below, we willdevelop a modified model to properly represent the dissolutionduring the stick-jump and the zipping-depinning modes.For the prediction of the contact angle θ2, it is important to
properly understand the movement of the contact line duringthe depinning−pinning transition. The duration of the zipping-depinning was found experimentally to vary from one ring toanother. We determine the average angular velocity ω = dc/tZD,where dc is the circumference of the ring and tZD the duration ofthe zipping-depinning process. We found a decrease of thevelocity of the ZDF for decreasing ring radii. In Figure 7, theexperimental data is shown. The scattering observed in the datais due to contamination and defects of the surface that pin theZDF between the rings.
Figure 6. Experimental data of the variation of the contact angle during the dissolution of a drop on smooth concentric rings separated 50 μm versusthe radius R and versus the volume V, respectively. We also show the prediction based on the conservation of volume during the jump, as proposedby Debuisson et al.1 (eq 2). The experimental data and theoretical prediction agree well at the early stage of the droplet dissolution, but not at laterstages. The red and black dotted lines in the graphs are only guidelines to the eye and show, respectively, the mismatch at later stages of dissolutionand the constant apparent depinning angle θ*.
Figure 7. Experimental measurements of the angular velocitycompared to the predicted values, as obtained from eq 8. A good fitis obtained for C = 4. The C = 1 and 8 values are also given forcomparison.
The velocity of the ZDF is governed by the dissolution rateof the droplet. To determine the velocity of the ZDF, weconsider a simple model for the geometry droplet; see Figure4c. The change of volume of the droplet can easily beapproximated using the expression for the volume of a sphericalcap; see Figure 4c.By subtracting the volume integrals of the two sectors of
spherical caps, we can determine the change in volume as afunction of ϕ. First, we integrate over the volumes of thesectors for the two radii R1 and R2 as
∫ ∫ ∫ ϕ
ϕ ϕ
=
= − ≕
ϕ
−
− −
⎜ ⎟⎛⎝
⎞⎠
V r z r
h R h R h
d d d
12
16
( , )
iR h
R r R h
i i i
0 0
2
2 3
i
i i i2 2 2
(3)
Therefore, the volume difference can be written as
ϕ
ϕ
= − = −
≕ Δ
V V V R h R h
R R h
( ( , ) ( , ))
( , , )ZD 1 2 1 2
1 2 (4)
R1, R2, and h are fixed for each pair of rings, which means thatthe change in volume is proportional to the angle ϕ with aconstant factor Δ = Δ R R h( , , )1 2 . We can write the timevariation dependence of the volume associated with the ZD asfollows
ϕ ω= Δ = ΔV
t td
ddd
ZD(5)
The dissolution rate is dominated by the diffusion driven masstransfer through the surroundings, as studied before by severalother authors.39,46−48 In this work, we calculate the diffusivedissolution of sessile drops, as proposed by Popov,46 using thefollowing expression
ρθ
θ θθ= − Δ
− +
⎡⎣⎢
⎤⎦⎥
Rt
D cR
fdd 2
( )2
2 3 cos cossin
d3
1/3
(6)
where46
∫θ θθ
θπ
π θ
= +
+ + ϵϵ
− ϵ ϵ
∞f ( )
sin1 cos
41 cosh(2 )
sinh(2 )
tanh[( ) ]d
0
(7)
is the geometrical shape factor used to model the effect of theimpenetrable substrate and θ is the macroscopic contact anglewith respect to the flat substrate.Thus, by calculating the dissolution rate dV/dt of a droplet
(eq 6) and calculating Δ from the known geometries, asproposed in eq 4, we can determine the angular velocity ω fromeq 5. The predicted and experimental values are shown inFigure 7. We can see that the experimentally determinedvelocity is always higher than the theoretically predictedvelocity. This underestimation can be due to a considerableenhancement of the dissolution rate that can be expected dueto the curved geometry during the zipping-depinning process,49
which has been ignored in our calculations. Additionally, it canbe influenced by the underestimation of the volume of oursimple geometrical model. To counteract this effect, in Figure 6,we have introduced a fitting parameter C, which is defined as
ω =
CV
t1 d
dZD
(8)
to account for an increase of the effective dissolution rate. Weassume that the scatter of the experimental data is due toimperfections of the substrate, showing occasional intermediatepinning points during the zipping-depinning process.To improve the predictions, we calculate the mass loss
during the transition from ring to ring using the expressionsabove. We compute the duration of the zipping-depinningprocess and evaluate the mass loss during this time to calculatethe new angle θ2. In Figure 8, we display the results of the newcalculations along with the experimental results, showing animproved agreement with the data during the whole dissolutiontime of the droplet.
■ CONCLUSIONSIn summary, we have studied the dissolution of sessilemicrodroplets on substrates patterned with concentric geo-metrical grooves. We report a novel zipping-depinning modethat occurs at the late stage of the dissolution of a dropletlocated on concentric ring patterns. The zipping-depinning
Figure 8. Experimental results for the contact angle versus the radius of the drop versus the radius R (left panel) and versus the volume V (rightpanel) and theoretical prediction by taking into account the volume loss during the jumps. A zoom highlights the difference between the previousmodel of ref 1 and the one proposed here. The new model takes into account the change in volume during each jump, in order to describe the thecontact angle behavior during the whole lifetime of the droplet.
takes place at a time scale one order of magnitude slower thanthat in the stick-jump mode. When the transition from thejumping to the zipping-depinning mode exactly occurs is still anopen question. In particular, one could wonder whether it is aqualitative transition between two fundamentally differentmodes or whether the jumping mode is reminiscent ofzipping-depinning, only occurring faster due to the change inthe relative scale of the grooves with respect to the droplet size.Resolving this subject would require high-speed imaging duringthe experiments, which goes beyond the scope of this article.The study and understanding of the zipping-depinning modeallows for the improvement of the existing techniques topredict the contact angle hysteresis due to the underlyingpattern. We have also demonstrated that the mode is controlledby the evaporative mass loss during the jumps. The dynamics ofthe contact line is directly related to the volume change andrestricted by the geometry imposed by the pinning at theconcentric rings. With our model, we can calculate the contactangles of the drop for the entire duration of the dissolution bytaking into account the volume change during the zipping-depinning mode.
■ APPENDIXThe microfabrication process for the samples is described in ref42 and is displayed in Figure 9. To form the micropatterned
concentric ring samples for the experiments, two different kindsof substrates, commercial Silicon wafers (Siltronix, France) andglass disks (Thermo Scientific, Germany), are processed byphotolithography, as depicted in Figure 9a−d, resulting in asmooth profile showed in Figure 9d. Figure 10 shows surfaceprofiling obtained by scanning electron and atomic forcemicroscopy. The techniques confirm a smooth profile of thering. The smooth profile SU-8 defects have a height of ∼560nm and a width of ∼5 m, i.e., an aspect ratio of ∼10. The rootmean square roughness of the SU-8 is ∼3 nm. The surfaceswere fabricated in a cleanroom.
■ ACKNOWLEDGMENTSWe would like to acknowledge Dr. Pengyu Lv for the fruitfuldiscussions and help as well as Javier Rodriguez Rodriguez forthe inspiring conversations and invaluable help. This work wassupported by the Netherlands Center for Multiscale CatalyticEnergy Conversion (MCEC), an NWO Gravitation programfunded by the Ministry of Education, Culture, and Science ofthe government of the Netherlands. X.Z. acknowledges thesupport from Australian Research Council (FT120100473 andLP140100594).
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Figure 9. (a−d) Scheme of the photolithography preparation processof the substrates with concentric rings using the photoresist SU-8 as apatterned substrate prepared on top of confocal microscopy glasscovers.
Figure 10. Scanning electron and atomic force microscopy images ofthe lithographic defect made using SU-8. (a) SEM of concentriccircles. (b) SEM zoom. (c) Three-dimensional atomic forcemicroscopy (AFM) image. (d) Profile obtained using AFM.
